Date: Jan 31, 2013 3:23 AM
Author: William Elliot
Subject: Re: Beating the Odds?

On Wed, 30 Jan 2013, wrote:
> On Wednesday, January 30, 2013 12:29:09 AM UTC-8, William Elliot wrote:

> > There is a fair coin with a different integer on each side that you can't
> > see and you have no clue how these integers were selected. The coin is
> > flipped and you get to see what comes up. You must guess if that was the
> > larger of the two numbers or not. Can you do so with probability > 1/2?

> Well, there was the monty hall problem years ago. Suppose there are 3
> keys and you have to choose one. One of the three turns on a car's engine
> where the other two do not. After you choose a key Monte takes one and
> tries it in the car and it doesn't turn over the engine. He then asks
> you if you'd like to change your mind. What should you do? You should
> change your mind because the first key you chose had a one in three chance
> of turning on the car where the remaining key has a two in three chance.
> Soo...
> Assuming the coin only has positive integers then you should guess
> the number showing is the smaller integer because there are more
> integers greater than x than there are less than x and this is true
> for all positive integers x.

Recall, you have no clue how the integers were selected much less that
both are positive or non-negative.

Here's a variant. Instead of integers, the coin has
a positive rational on each side.